Unbiased Black-Box Complexity of Parallel Search

  • Golnaz Badkobeh
  • Per Kristian Lehre
  • Dirk Sudholt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8672)

Abstract

We propose a new black-box complexity model for search algorithms evaluating λ search points in parallel. The parallel unbiased black-box complexity gives lower bounds on the number of function evaluations every parallel unbiased black-box algorithm needs to optimise a given problem. It captures the inertia caused by offspring populations in evolutionary algorithms and the total computational effort in parallel metaheuristics. Our model applies to all unary variation operators such as mutation or local search. We present lower bounds for the LeadingOnes function and general lower bound for all functions with a unique optimum that depend on the problem size and the degree of parallelism, λ. The latter is tight for OneMax; we prove that a (1+λ) EA with adaptive mutation rates is an optimal parallel unbiased black-box algorithm.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Golnaz Badkobeh
    • 1
  • Per Kristian Lehre
    • 2
  • Dirk Sudholt
    • 1
  1. 1.University of SheffieldUK
  2. 2.University of NottinghamUK

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